Wall Street isn’t sold on a short-term plan to deal with the debt ceiling.

While the stock market Thursday had its second-biggest gain of the year after Republicans proposed a temporary increase in the nation’s borrowing limit, many investors remained deeply skeptical that a six-week extension will be enough to end the budget stalemate.

And that was before President Obama rejected the GOP plan late Thursday because it would not end the 10-day-old government shutdown.

The Dow Jones industrial average and the Standard & Poor’s 500 both jumped 2 percent on the Republican proposal to increase the debt limit through Nov. 22, in exchange for negotiations with Democrats on spending cuts and other concessions.

The blue-chip index gained 323 points to close at 15,126.07, although it remains 5 percent below its Sept. 18 high. The S&P 500 closed at 1692.56, off about 2 percent from its peak.

Indeed, the smart money is signaling that six weeks is not long enough to come up with a compromise that has eluded the two parties for years.

“Keep in mind that we have had two Blue Ribbon panels present budget reform plans under this divided government, each of which has been ignored,” said Steven Ricchiuto, the chief economist of Mizuho Securities USA.

“It is hard to see what has changed in the calculus of power on the Hill that will lead to a successful compromise over the next six weeks or so.”

Added one hedge-fund executive: “If they offered 90 days maybe, but six weeks doesn’t work.”

The problem for worried market-watchers is that the six-week deadline would end Nov. 22 — smacking right up against Thanksgiving and the busy Christmas retailing season.

There is no reason to think the US won’t be facing the same drama then as now, said Jerry Webman, OppenheimerFunds’ chief economist.

He noted that while stock markets have rallied, the debt markets have taken a more measured approach to the signs of progress in the budget impasse. The benchmark 10-year Treasury note yield rose 1 percent to close at 2.68 percent, a move opposite of equities and more cautious on the debt-ceiling outcome.

“Repo rates — all the interbank stuff — shot up and haven’t come down that far,” he said.

Those rates went from 0.08 percent on Oct. 2, the day the government shutdown began, to 0.24 percent Wednesday before falling to 0.22 percent Thursday, he said.

Treasury bills due Nov. 7 — short-term funding most likely to get hit by a default — went from a rate of 0.125 percent the week of Oct. 8 to 0.30 percent by Wednesday and only fell back to 0.24 percent Thursday, he said.

But the most savvy investors are still taking the problems in stride. Those with cash on hand said they will look for buying opportunities in any weakness.

“Investors have been living with government risk at least since the financial crisis,” said Dan Arbess, a partner at Perella Weinberg Partners. “Day-trading headlines and rumors is not an investment strategy, but being patient and buying when things get choppy should produce good results.”